Blender use texture on cube side
I am no specialist for exporting other formats (like .fbx), but in general it's like this:

To add a texture only to the side you will need a second material.

Click the material tab and click + to add a new material.
Then click + New.

Get into Edit-Mode and select the face you want to apply the material to.
With it selected click Assign under the materials.

This will assign the new Material only to that specific face.

Keep the new material selected in the material tab.
Then click the texture tab and add your texture to it by clicking + New, selecting Image or Movie(should be default) and sroll down to Image and Open your Image Texture.

Positioning of the texture can be performed by the options below the Image part.